Typical electrical power utility systems use a network of power generators to provide electrical power via transmission lines in a transmission grid, to numerous loads. Each generator generates electrical power in response to a real input mechanical power, such as that provided by steam pressure or water flow, and an excitation control system which provides a reactive power output and which ensures that the generator provides a desired target voltage for each transmission line. A problem to be solved by a control system for such an electrical power utility system (hereafter simply a "power system") is maintaining the power system in equilibrium in spite of transients, which may cause the network of generators to go into mechanical oscillation in response to excess electrical energy being fed into the grid during the transient. That is, despite these transients, it is necessary, if the integrity of the power specifications are to be maintained, that each generator be kept operating at an angular velocity and a rotor angle (the angle between a point on the generator shaft and some arbitrary, synchronously rotating reference, such as a clock reference signal, defined for the generator network) which insures that the electrical output power matches the mechanical output power and that voltage limits of the generator are not violated.
Furthermore, any control must stabilize power system transients in the first few seconds subsequent to the transient, during a period of time when the system may have changed drastically, and/or may be subject to multiple transients, due to multiple transmission line reclosures or cascading equipment losses.
System changes or disturbances, causing transients for which a control system must compensate, are changes in the network configuration, loading and power transfer characteristics--e.g. loads being added to or removed from the transmission network, generators being added to or removed form the network (e.g., due to failures) and transmission lines being connected to or disconnected from the grid (e.g., due to storm damage). Mechanical oscillations of the generators resulting from transients due to such changes are highly undesirable. They must be damped and excess energy must be dissipated. System changes or disturbances may also cause the equilibrium point of the power system to change.
A further problem to face when designing a control system is anticipating that a power system may be loaded beyond its original design specifications. When a power generating center is geographically removed from a major center of power consumption such loading is increasingly common. Much of the motivation to transfer large amounts of power is economic, arising out of efforts to maximize power generation from nuclear and hydroelectric plants and to lighten the load on more expensive fossil-fuel plants. Thus, the development of more effective controls translates directly into more economical operation of the power system.
However, increased loading results in increasingly heavy power transfers over long transmissions lines. The transmission lines are thus operated closer to maximum power transfer limits, as defined by power flow equation. Stability problems, resulting from such heavy transmission line loading, further limit the operation of a power system. Moreover, synchronizing torque, generated by a swing in the generator rotor angle away from the equilibrium position, is not only weaker in terms of the change of output power for a unit change and rotor angle, but also becomes more nonlinear as a transmission line approaches its transfer limit.
As transmission line loading increases, a system may also exhibit a tendency towards poorly-damped oscillations, involving the rotor angles of many generators in widely separated areas (so-called multimachine or winter-area oscillations), that occur predominantly in a frequency range of approximately 0.5-0.8 Hz. These factors may limit the amount of transferable power to a value well below the thermal limit of the transmission line, because of the need to assure the integrity of the power system in the event of transients. For a given operating condition, if the integrity of a power system cannot be assured for any reasonably foreseeable transient, then its control system is not viable for normal operation, even though it may be nominally stable. Poorly damped oscillations of the type described have been experienced in the western and northeastern areas of the United States, and in many systems world wide.
The mechanism behind inter-area oscillations of generators is not fully understood, however there have been conjectures that they may be a result of nonlinear coupling phenomenon. They may be aggravated by improper control system design. The problem may also be linked to the problems of voltage instability that occur on heavily-loaded transmission lines that have insufficient reactive power support. That is, a lack of reactive power support, coupled with low load-bus voltages, may create a "voltage collapse" situation in which load-bus voltages decline at the same time that generators hit power transfer limits, further reducing the capability for existing types of control to damp electromechanical oscillations. Such electromechanical oscillations directly constrain the operation of many power systems.
In order to design more effective control, a major limiting factor is the lack of power system information available to any given controller. This information is limited to locally available measurements due to difficulties in transmitting measurements over large distances. The limits on available information have a direct impact on the ability to design sufficiently robust and reliable linear controllers. The anticipation of large changes to a power system also should be considered. Any practical control for stabilizing transients therefore should be designed to use only information that is available at the site of the controller.
It should be further recognized in the design that there will be large disturbances that will push the system beyond the limits of the validity of a small-signal model. Often these disturbances are accompanied by structural changes in the system itself. A linear approximation of the system that is acceptable for one operating condition may be rendered completely inaccurate by either slowly evolving load changes or by step changes that occur as a result of power system faults. Consequently, any controller that relies upon a given static model may not operate satisfactorily as the power system changes.
Some work has been done in the area of online power system identification for the purpose of control, but since the order of a power system is generally unknown, and can change instantaneously, an assumed order that is used for estimation of the external system may result in a good approximation one minute and a poor one the next. The rate at which accurate estimation may occur is limited by the fact that there are many orders of dynamics that are ignored based on time scale separation. Raising the sampling rate of an estimator causes the faster dynamics of the power system to affect the estimate. Given the fact that good control is most critical at exactly when the system model is most uncertain, trade-offs must be made between modeling inaccuracies and optimal control and robustness. In addition, since many of the control schemes that have been proposed perform closed-loop identification, and generally have been formulated in the theoretical framework of adaptive control, the issues of control stability beyond the empirical evidence of low-order simulations are largely unanswered.
Efforts have been made to utilize devices such as fast reactive power compensators (e.g., static VAR compensators) and high voltage DC tie lines in order to enhance system damping, using various types of linear controllers. Reactive power compensators have traditionally been used to maintain a near-constant voltage on a give bus. HVDC tie lines maintain a near-constant real power transfer. Recent work indicates that a more integrated systems approach to the overall network control problem may result in more effective use of these devices for stable system operation.
The shift in emphasis in the use of voltage support equipment for stability enhancement has been away from the concept of maintaining a constant voltage at the device terminals, toward the use of the device's reactive power capacity as a means of stabilizing oscillations in transferred power, at the expense of some fluctuation in the terminal voltage. This is the purpose of a power system stabilizer (PSS), which modulates the setpoint of a generator voltage controller to achieve a gain in stability.
Current state of the art power system stabilizers (PSS) do not require any a priori knowledge of the post-disturbance equilibrium point and operate as linear, constant gain devices. A PSS develops a voltage correction term that is added to a constant voltage reference term. This sum is compared to the actual generator terminal voltage to arrive at a voltage error signal for the voltage regulator (or exciter) of the generator. A common type of PSS is shown in FIG. 1. It includes a prime mover 10, such as a turbine, which provides real mechanical input power, in response to steam pressure of water flow, to a generator 12. The generator has a shaft (not shown) whose rotation speed is determined by a shaft speed transducer 14. The exciter 16 modulates the generator excitation, in response to a voltage error signal, so that the generator terminal voltage matches the target voltage. The voltage error signal is determined (in the illustrated system) based upon a speed or frequency error signal, by comparing a reference speed 18 to the shaft speed such as with a simple adder 20. The shaft speed error signal is applied to the PSS 22, which uses one or more linear control functions to produce an output voltage correction term. The output of the PSS is substrated, with a simple adder 26, along with the determined generator voltage, from a voltage reference 24 to provide a voltage error signal which is provided to the exciter 16.
A typical PSS is thus used to provide damping torque, which is analogous to the viscous damping of a spring-mass-dashpot system. The PSS is normally tuned to provide damping at some critical frequency of machine oscillation, and some effort is typically made to assure that other potential oscillation modes are not aggravated by the selected tuning parameters. Because of the difficulty of generating a signal representing the error in the generator rotor angle, this signal is not used as an input to typical power system stabilizers. The characteristics of these PSS vary significantly with transients in the power system. In particular, since the power system is nonlinear, a system change may render non-optimal an optimal, linear PSS. That is, the tuning of the PSS may become invalid, and may become troublesome in stabilizing the power system after a large transient.
All of the above methods achieve some improvement in power system stability, but all are limited by robustness problems due to the nonlinearity of the power system. As the transmission line approaches the maximum power transfer limit, the range of accuracy of small signal models (i.e., linearized models) that form the basis for linear controllers becomes progressively more limited. Moreover, some aspects of the power system are highly nonlinear precisely when the power system is most likely to be unstable, i.e, when damping large oscillations occurring over heavily loaded transmission lines. In view of these problems some researchers have proposed nonlinear control systems for synchronous generators.
One well-known type of nonlinear control system is called feedback linearizing control (FBLC). The general form of FBLC is well documented, and theoretical background may be found in Applied Nonlinear Control, Prentice Hall, 1991, by J.-J. E. Slotine and Weiping Li.; Nonlinear Control SystemsSpringer-Verlag, 1989 by Alberto Isidori; F. K. Mak and M. D. Ilic, "Towards most effective control of reactive power reserves in electric machines", pages 359-367, Graz, Austria, August 1990, 10th Power System Computation Conference; and "A new class of fast nonlinear voltage controllers and their impact on improved transmission capacity", American Control Conference, 1989 by M. Ilic and F. K. Mak.
FBLC forces the generator dynamics to obey the following differential equation: EQU .omega.=a.sub.0 (.delta.-.delta..sub.0)+a.sub.1 (.omega.-.omega..sub.0)+a.sub.2 .omega. (1)
where .omega. represents the frequency of the AC voltage of the machine, and .delta. represents the rotor angle of the generator in the Park/Blodel transformed frame of reference. A derivative of a variable, e.g., .omega., with respect to time is represented as .omega.. .delta. satisfies the relationship: EQU .delta.=.omega.-.omega..sub.0 ( 2)
The coefficients a.sub.0, a.sub.1 and a.sub.2 in (1) are selected based on well established linear systems theory to achieve a stable system with desirable transient response characteristics.
The equilibrium point of this subsystem is at .omega.=0, which can only be satisfied when EQU .omega.=0 (3) EQU .omega.=.omega..sub.0 ( 4) EQU .delta.=.delta..sub.0 ( 5)
Although this equilibrium definition also holds 4 or a linearized control system such as the PSS, linear systems do not base control on this definition. The value of .omega..sub.0 is fixed by the power system frequency, but value of .delta..sub.0 depends on the configuration and loading of the system and, in general, cannot be calculated without full knowledge of the system voltages, loading and configuration, and even then requires a computationally intensive calculation. Moreover, .delta..sub.0 can only be measured with respect to a power system wide reference which cannot be maintained as a local measurement. Since the value of .delta..sub.0 must be available to the FBLC exciter for proper operation, and in particular, since the use of an invalid rotor angle reference causes loss of control of the generator voltage, FBLC is impractical unless the problem of computing or measuring .delta..sub.0 can be resolved.
All methods of FBLC presented to date have been limited by the fact that the desired post-disturbance equilibrium point for the generator must be known a priori, if the control is to work properly on a system having many generators. The information that can be used for the generator control is limited primarily to measurements that can be made locally at the site at which the generator is located. Unfortunately, the loading and configuration of the entire system, which cannot be determined locally, must be known in order to calculate the equilibrium point for any given generator. Since the desired equilibrium point changes with every change in the system, any practical control must be capable of responding to the system changes, which occur frequently. No mechanism has previously been developed for FBLC controllers to adjust to the evolution of the equilibrium point of a generator over time, without relying upon information from distance parts of the system that is normally unavailable. Thus, there is typically not enough information available to assure that the power system is stabilized after a large transient while assuring that the generator terminal voltage returns to a preset value.
In 1981, a different nonlinear control system (the Observation Decoupled State Space, or, ODSS) was proposed by J. Zaborszky, K. V. Prasad, and K. W. Whang, in "Stabilizing control in emergencies", part 2, IEEE Transactions on Power Apparatus and Systems, PAS-100(5):2381-2389, 1981. In ODSS, the equilibrium point of the power system is estimated, including a calculation of an estimated .delta..sub.0 (i.e., rotor angle), based on local measurements of voltages and phases of transmission lines connected to the generator. This system is based on the solution of the equilibrium equation: EQU P.sub.m -P.sub.e =0 (6)
where P.sub.m is the mechanical input power and P.sub.e is the electrical output power. This may be expressed a function G which represents the mismatch, or difference, between the generator input power and electrical output power. G may be expressed as a function of all of the line voltages V.sub.i and phases .theta..sub.i of K connected transmission lines: EQU G(V.sub.1, . . . , V.sub.K, .theta..sub.1, . . . , .delta..sub.r, . . . , .theta..sub.k)=0 (7)
and which includes measuring the generator terminal voltage. These equations are solved to yield an estimated equilibrium rotor angle .delta..sub.r.
ODSS relied on fast modulation of the real input power (or torque) to the generator or on fast control of the electrical output power via braking resistors and load skipping. Load skipping means that loads are switched on and off in short pulses. Braking resistors are networks of large resistors that are used to dissipate large amounts of power. There are many practical difficulties with this control system, however. First, all the methods for fast real power control, (i.e., for controlling the real input power or torque) are very expensive and create significant mechanical stress on the generator shaft. The potential for damage from torsional oscillations of the generator shaft compounds this problem. These control actions are also not especially flexible. For instance, both load skipping and braking resistors can only be used in short, discrete pulses.
A feature of ODSS is the estimation of the equilibrium rotor angle .delta..sub.r using only local measurements, including the use of a locally generated reference signal based on the nominal system frequency (e.g., in the U.S., 60 Hz). The reference signal does not need to be synchronized to any other part of the power system. It therefore provides a method for generating a rotor angle error signal based upon a direct measurement of the shaft position, with respect to the phase angle of the reference signal. This is a departure from conventional methods that require all angles to be measured with respect to a system wide reference.
A further drawback of ODSS, however, is that the estimation of .delta..sub.r assumes that the terminal voltage of each generator was both separately controlled and constant. The estimation of .delta..sub.r is unstable when used to control the terminal voltage of the generator. More generally, the proposed calculation is unstable when variations in the local generator voltage are dynamically coupled to large power system transient behavior.
Accordingly, it is the general aim of the invention to provide an excitation control system for an electrical power utility system, which controls the generator voltage using an approximation of the equilibrium rotor angle.
It is also an object of the present invention to provide an excitation control system for a power utility system which increases power transfer capability on existing transmission lines.